1. Field of the Invention
The present invention relates, in general, to error correction in communication systems such as errors produced in channels in wireless or digital radio communications between devices, and, more particularly, to software, systems, and methods for decoding tail-biting convolutional codes at a receiver, such as an uplink receiver for an orthogonal frequency division multiplexing access (OFDMA) communication system or network.
2. Relevant Background
There are ongoing efforts to provide next generation mobile communications and to improve existing communications among networked devices including among wireless devices. A recent development has been to not only do away with wires or cables within a building or home but also to do away with the cables coming into the building or home. WiMAX technology (also known as 802.16 because it is based on the IEEE 802.16 WirelessMAN Standard for Wireless Metropolitan Area Networks) promises to allow this jump to more wireless communications that function as a wireless alternative to cable modems and DSL (Digital Subscriber Line). WiMAX will likely offer connectivity at up to 30 miles from an antenna at speeds up to 75 mbps (megabytes per second) and at higher rates or speeds under 5 miles, whereas a cable modem may only offer speeds of 1 mbps. As a result, where cable and telephone companies do not offer broadband Internet connections, WiMAX technology offers a way to provide broadband Internet, digital TV, and other digital communications with the use of a wireless antenna to pick up a WiMAX signal that is then distributed wireless (or with wires) throughout the local area by a base station (BS) to user terminals or devices (e.g., to subscriber stations (SSs)). The OFDM (Orthogonal Frequency Division Multiplexing) technique has been widely proposed in WiMAX and many other wireless systems to provide high data rate transmission. OFDM uses a set of overlapping but orthogonal sub-carriers to realize high spectrum efficiency. More recently, combined with TDMA (Time Division Multiple Access) and/or FDMA (Frequency Division Multiple Access), OFDMA has been proposed in many broadband wireless systems such as WiMAX systems.
An ongoing challenge in any communication system, including WiMAX systems such as those defined by IEEE 802.16d/e, is how to correct errors in the signal between a transmitting device and a receiving device. Information signals or data transmitted between a transmitter and a receiver via a communication channel can be corrupted, i.e., errors can be introduced into the signal or data before it is received at the receiver. A communication channel is any medium (wired or wireless) between a transmitter and a receiver. The medium may introduce noise, interference, or other channel errors, and any medium that may inject errors can be thought of as a channel. The medium may be a storage medium or a communication or data transfer medium. In a practical radio communication system, noise is also picked up by the antenna or is generated within the front end amplifiers of the receiver. So, effective methods must be taken to correct errors generated by adding all these kinds of noise on a received signal.
Error detection and error correction codes are widely employed in digital communication systems to ensure the transmission reliability, and such codes are typically provided by channel encoding and decoding, i.e., an encoder in the transmitting device and a decoder in the receiving device. The use of such error correction acts to assist in protecting against channel errors, which occur in situations such as where there is noise, fading, multipath and interference such as when signal transmission or reception is in an elevator, in a moving car, amidst tall buildings, in hilly terrain, or the like. By adding redundancy or redundant bits into the transmitted information bits, error control techniques enable receivers to detect or even correct the errors introduced by channel distortion. While it is useful to add redundant bits to facilitate error correction, transmission of the redundant bits also consumes additional bandwidth and their number should be limited where possible to limit bandwidth usage.
One well-known technique for error-correction is by encoding the transmitted signal or data using convolutional codes (CC). Convolutional codes are generally described by a coding rate, a constraint length, and generator polynomials. In a convolutional encoder, each input bit travels through each memory element such that the number of output bits generated by the encoder corresponds to the number of input bits and the coding rate of the convolutional encoder. One method of convolutional encoding is to use “tail bits” to flush the encoder by initializing each memory element with a zero (e.g., to force a reset to the zero state) and the tail bits are added at the end of the input frame or stream as tails, which caused the increase of frame or stream length. FIG. 1 illustrates an example of a tail bits convolutional codes encoder 100 that receives an input stream of bits 102, has two memory elements 104, 106, two adder circuits 108, 110, and produces two output bits 120. The encoder 100 has a coding rate of ½ and a constraint length of 3, and as shown at this rate, one bit input 102 produces two bits output 120. It should be pointed out that the actual output bit 120 is not only related to the actual input 102 but also is related to the previous inputs from memory of the encoder or transmitter embodying the encoder 100. As a tail bits convolutional codes encoder 100, its shift registers shall be initialized by a definitive code (in most cases, an all-zero code), and this code is appended to the end of the information block to be encoded, which ensures that the encoder has the same starting state and ending state.
A well-known decoding technique performed at a receiver for convolutional codes is the Viterbi algorithm (VA) based on a trellis. FIG. 2 shows a trellis structure 200 of tail bits convolutional codes, i.e., for the encoder structure 100 in FIG. 1. The two shift registers 104, 106 of the encoder 100 will generate four different states at one stage in the trellis 200. The nodes in each column stand for the different states at each stage. The solid lines represent the state transition if the input bit is 0; while the dotted lines represent the state transition if the input bit is 1. The two values in the parentheses above these lines are the corresponding outputs. The fundamental idea of the VA is to obtain the minimum distance (or path metric) path from a starting state to an ending state. The distance is calculated between the decoding input and the output in the corresponding location of the trellis and stored in decoder memory (or receiver memory) as a branch metric. An Add-Compare-Select (ACS) process is taken to select a survival path. The branch metric accumulated along a survival path is denoted as a path metric. For each state at one stage, there will be only one survival path and one relevant path metric value. For instance for the encoder shown in FIG. 1, since both the starting state and ending state are “00”, the survival path must begin and end at the state “00”. At the end of the last stage, the VA starts from the state “00” and traces back to the state “00” at the first stage to retrieve the final decoding outputs.
An ACS process 300 for the VA is detailed in FIG. 3. The value above the state is designated for the path metric; while the value above the transition branch is for the branch metric. Two branches merge into one state in the ACS process 300. On the assumption that the VA is determining the survival path on the state “00” at the k-th stage, it needs to compare the accumulated path metrics of the “up” branch and the “down” branch. For example, the up branch merging into the state “00” at the k-th stage derives from the state “00” of the (k-1)-th stage. The path metric value on the state “00” of the (k-1)-th stage is 0.22, and the branch metric of the transition between these two states is 0.11. Thus, the up path metric on the state “00” at the k-th stage is accumulated to 0.33 (i.e., 0.22+0.11). In the same way, the down path metric on the state “00” at the k-th stage is accumulated to 0.22 (i.e., 0.16+0.06). After comparing the up and down path metrics, the VA decides to take the down path, i.e. the smaller one, as the survival path and saves the value 0.22 as the path metric on the state “00” at the k-th stage. The same operations are taken on the other states at the k-th stage.
As mentioned above, the tail bits convolutional codes encoder has a priori knowledge of starting and ending state in trellis diagram, which makes the VA useful for easily and reliably decoding tail bits convolutional codes. However, the appended tails reduce the bit rate to some extent since the tail bits must also be passed through the encoder. In order to maintain a higher bit rate, tail-biting convolutional codes have been proposed for use in encoding to provide forward error correction in communication systems.
FIG. 4 illustrates an exemplary encoder 400 employing tail-biting convolutional codes with a coding rate of ½ and a constraint length of 3. The encoder 400 receives an input bit stream 402, includes a pair of memory elements or shift registers 404, 406 and a pair of adder circuits 408, 410, and outputs to output bits 420. Different from the previous tail bits CC encoder 100, its shift registers 404, 406 are initialized by the last 2 bits of the information 402 to be encoded. The encoder 400 still guarantees that the starting and ending states are the same in its trellis, but the decoder 400 has no knowledge of the starting and ending states before decoding, which makes the decoding process much more complex than that of signal or data stream received from a tail bits convolutional codes encoder.
FIG. 5 illustrates the trellis diagram structure 500 of tail-biting convolutional codes when the VA is used for decoding. The decoder of tail-biting convolutional codes is only aware that the starting state and the ending state will be the same. One possible decoding method is to try all the states as a tentative starting state on one-by-one basis. For each starting state, the decoder would find the path with minimum path metric at the last stage as a tentative survival path. After trying all the starting states, the tentative survival path with the same starting state and ending state would be regarded as the final survival path. However, such a decoding algorithm or technique would need to perform the VA from the first stage to the last stage for 2km time (where “m” stands for number of input bit in one instant and “k” for the shift register size). As a result, such a decoding method is far too complex to satisfy a real-time system software implementation, such as in a digital signal processor (DSP) of a communication system receiver.
The communication industry continues, therefore, to demand a low-complexity tail-biting CC decoding algorithm with a sound error protection performance. This search for an improved decoding method, and decoders embodying such a decoding method, has more recently become even more important. This is because tail-biting convolutional codes have the advantage of saving bit rate without adding special tail bits to the encoded block. As a result, these encoding techniques have been adopted as standards for certain types of communication systems. For example, it has been used to encode the short message in North American Digital Cellular Radio (IS-54). Additionally, WiMAX systems are expected to become increasingly important in the wireless communication industry, and tail-biting convolutional codes have been adopted as a mandatory forward error correction scheme in the OFDMA mode of IEEE 802.16d/e systems.
Existing decoders have not satisfied all of the demands of the communication industry, e.g., the demands for lower computational complexity and for reduced memory usage by the decoder. For example, one proposed decoding method [R. V. Cox and C-E. W. Sundberg, “An Efficient Adaptive Circular Viterbi Algorithm for Decoding Generalized Tail-biting Convolutional Codes”, IEEE Transactions on Vehicular Technology, Vol. 43, No. 1, pp. 57-68, February 1994] includes starting from all the states, saving the corresponding best-trellis-path, and decoding a metric score each time. The method then continues with comparing all the saved decoding-metric-scores to select the best one and then, giving out its corresponding output bit stream as the correct and most likely decoding result. However, such a decoding method is too complex for implementation in real-time communication applications and systems as it involves the standard Viterbi algorithm being performed 2mk times.
Two other proposed decoding schemes, i.e., the “Bar-David” scheme and the “two-steps scheme,” also fail to address the concerns of the communications industry [H. H. Ma and J. K. Wolf, “On Tail Biting Convolutional Codes”, IEEE Transactions on Communications, Vol.COM-34, No. 2, pp. 104-111, February 1986; Q. Wang and V. K. Bhargava, “An Efficient Maximum Likelihood Decoding Algorithm for Generalized Tail Biting Convolutional Codes Including Quasicyclic Codes”, IEEE Transactions on Communications, Vol. 37, No. 8, pp. 875-879, August 1989]. In the Bar-David decoding method, the processing steps include: (1) choosing an arbitrary starting state; (2) decoding using a maximum likelihood decoder which finds the best path from that starting state to all possible ending states; (3) checking the decoded code word to see if the starting state is the same as the ending state and if yes, stopping, otherwise going a next step; (4) using the previous ending state as the new starting state, checking to see if this starting state has been tried before, and if yes, going to step 1, otherwise returning to step 2. The Bar-David method has a number of disadvantages. The standard Viterbi algorithm needs to be performed at least twice, except that the first chosen starting state is just the real starting state. In non-optimum occasions, the Bar-David computational complexity is the same as that in other proposed methods (i.e., repeating the VA algorithm 2mk times), and so, this method is still too complex for implementation and real-time application. In the proposed two-step method, the processing steps include: (1) obtaining an ordered list of the 2mk starting states using an algebraic method called “continued fractions” and (2) performing the VA using each entry on the ordered list as their starting state. Again, this method requires the VA to be run many times and as a result, it is too complex for most practical communications applications.
Several decoding schemes for tail-biting convolutional codes have been suggested in issued patents, but none have been widely adopted by industry, which is likely due to their significant computation complexities and memory usage. For example, U.S. Pat. No. 6,256,764 to Atallah describes a process involving: (1) giving the same possibility to all the starting states; (2) performing the Viterbi algorithm once to find an ending state with lowest ending score and making a list including all the ending states within a certain value range to the lowest ending score; (3) performing the Viterbi algorithm with every list state as a starting state and recording the corresponding score; and (4) comparing all the recorded scores of the last step, selecting the lowest one, and saving it as the real ending and starting state. Again, this method requires that the Viterbi algorithm be run many times, which increases its computational complexity.
U.S. Pat. No. 6,877,132 to De et al. describes a decoding method that includes the steps of: (1) modifying the input bit stream by repeating part of the input decoding bits; (2) assuming a probability for each possible initial state of the encoder; (3) decoding each symbol of the input decoding bit stream using majority logic with reference to a trellis structure corresponding to the encoder; and (4) reorganizing the output bit stream according to the rules of used for modifying the input bit stream. This method has a number of disadvantages including the bit stream needing to be modified both before and after decoding and the Viterbi algorithm needing to be performed many times with relatively high complexity. As a result, this method does not provide a useful general decoding algorithm for tail-biting convolutional codes.
U.S. Pat. No. 5,349,589 to Chennakeshu et al. describes another decoding method, but as with the other methods discussed above, this method has not been widely adopted by the communications industry. The decoding method includes: (1) separating an encoded frame of data into key bits, critical bits, and unprotected bits in which the key bits and critical bits in the received stream are encoded with tail-biting convolutional codes and are merged with unprotected bits; (2) splitting the received data into convolutionally encoded bits and unprotected accordingly; and (3) starting from all the possible states, decoding the convolutionally encoded bits into a number of possible paths using a generalized Viterbi algorithm and then finding the path which provides a lowest path metric. This method is not entirely acceptable for implementation in standards-based encoders and decoders because both the encoding and decoding data are special. Hence, this method does not provide a general decoding algorithm useful for tail-biting convolutional codes.
From this discussion, it can be seen that these suggested decoding methods typically perform the VA repeatedly until an end state matches a starting state, with the main difference between the methods being the way the search for the real starting state is performed. The number of VA iterations is generally so high that these methods are undesirably complex for implementation in a real-time software application, such as would be used in a digital signal processor (DSP) of a communication receiver. In bad channel conditions (such as those with a low signal to noise ratio), the trellis or decoding path that has the same starting state and ending state may not even exist, which causes the aforementioned methods to simply not work.
Hence, there remains a need for an improved method, and associated decoders, for decoding data that has been encoded using tail-biting convolutional codes. Preferably, such a decoding method would be designed with lower computational complexity and memory usage when compared with prior decoding schemes, and further, it is preferable that such a decoding method would be well-suited for use in standard communication systems and networks, such as in WiMAX and other wireless receiving devices (e.g., an OFDMA mode device and the like) including those configured according to the IEEE 802.16 standard.